# Logical Unification
[](https://travis-ci.org/pythological/unification) [](https://coveralls.io/github/pythological/unification?branch=main) [](https://pypi.org/project/logical-unification/)
[Logical unification](https://en.wikipedia.org/wiki/Unification_(computer_science)) in Python, extensible via dispatch.
## Installation
Using `pip`:
```bash
pip install logical-unification
```
To install from source:
```bash
git clone git@github.com:pythological/unification.git
cd unification
pip install -r requirements.txt
```
Tests can be run with the provided `Makefile`:
```bash
make check
```
## Examples
`unification` has built-in support for unifying most Python data types via the function `unify`:
```python
>>> from unification import *
>>> unify(1, 1)
{}
>>> unify(1, 2)
False
>>> x = var()
>>> unify((1, x), (1, 2))
{~x: 2}
>>> unify((x, x), (1, 2))
False
```
Unifiable objects containing logic variables can also be reified using `reify`:
```python
>>> reify((1, x), {x: 2})
(1, 2)
```
And most Python data structures:
``` python
>>> unify({"a": 1, "b": 2}, {"a": x, "b": 2})
{~x: 1}
>>> unify({"a": 1, "b": 2}, {"a": x, "b": 2, "c": 3})
False
>>> from collections import namedtuples
>>> ntuple = namedtuple("ntuple", ("a", "b"))
>>> unify(ntuple(1, 2), ntuple(x, 2))
{~x: 1}
```
Custom classes can be made "unifiable" with the `unifiable` decorator:
```python
@unifiable
class Account(object):
def __init__(self, id, name, balance):
self.id = id
self.name = name
self.balance = balance
>>> data = [Account(1, 'Alice', 100),
Account(2, 'Bob', 0),
Account(2, 'Charlie', 0),
Account(2, 'Denis', 400),
Account(2, 'Edith', 500)]
>>> id, name, balance = var('id'), var('name'), var('balance')
>>> [unify(Account(id, name, balance), acct) for acct in data]
[{~name: 'Alice', ~balance: 100, ~id: 1},
{~name: 'Bob', ~balance: 0, ~id: 2},
{~name: 'Charlie', ~balance: 0, ~id: 2},
{~name: 'Denis', ~balance: 400, ~id: 2},
{~name: 'Edith', ~balance: 500, ~id: 2}]
>>> [unify(Account(id, name, 0), acct) for acct in data]
[False,
{~name: 'Bob', ~id: 2},
{~name: 'Charlie', ~id: 2},
False,
False]
```
`unification` also supports function dispatch through pattern matching:
```python
>> from unification.match import *
>>> n = var('n')
@match(0)
def fib(n):
return 0
@match(1)
def fib(n):
return 1
@match(n)
def fib(n):
return fib(n - 1) + fib(n - 2)
>>> map(fib, [0, 1, 2, 3, 4, 5, 6, 7, 8, 0])
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34]
```
The pattern matching can be fairly complex:
```python
>> name, amount = var('name'), var('amount')
@match({'status': 200, 'data': {'name': name, 'credit': amount}})
def respond(name, amount):
balance[name] += amount
@match({'status': 200, 'data': {'name': name, 'debit': amount}})
def respond(name, amount):
balance[name] -= amount
@match({'status': 404})
def respond():
print("Bad Request")
```
See the full example in the [examples directory](https://github.com/pythological/unification#examples).
## Performance and Reliability
`unification`'s current design allows for unification and reification of nested structures that would otherwise break the Python stack recursion limit. It uses a generator-based design to "stream" the unifications and reifications.
Below are some stack vs. stream benchmarks that demonstrate how well the stream-based approach scales against the stack-based approach in terms of unifying and reifying deeply nested lists containing integers. These benchmarks were generated from the tests in `tests/test_benchmarks.py` using CPython 3.7.3.
<details><summary>Stack vs. stream benchmarks</summary>
<p>
```python
-------------------------------------------------------------------------------- benchmark 'reify_chain size=10': 2 tests -------------------------------------------------------------------------------
Name (time in us) Min Max Mean StdDev Median IQR Outliers OPS (Kops/s) Rounds Iterations
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
test_reify_chain_stack[10] 41.0790 (1.0) 545.1940 (3.20) 52.9087 (1.07) 9.7964 (1.04) 50.8650 (1.08) 6.4301 (8.37) 11815;10849 18.9005 (0.93) 260164 1
test_reify_chain_stream[10] 42.4410 (1.03) 170.5540 (1.0) 49.3080 (1.0) 9.3993 (1.0) 47.2400 (1.0) 0.7680 (1.0) 14962;102731 20.2807 (1.0) 278113 1
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
------------------------------------------ benchmark 'reify_chain size=1000': 1 tests -----------------------------------------
Name (time in ms) Min Max Mean StdDev Median IQR Outliers OPS Rounds Iterations
-------------------------------------------------------------------------------------------------------------------------------
test_reify_chain_stream_large[1000] 7.7722 28.2579 10.0723 2.5087 9.4899 0.3106 70;155 99.2820 1528 1
-------------------------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------- benchmark 'reify_chain size=300': 2 tests --------------------------------------------------------------------------
Name (time in ms) Min Max Mean StdDev Median IQR Outliers OPS Rounds Iterations
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
test_reify_chain_stack[300] 1.5183 (1.0) 22.1821 (1.19) 1.9826 (1.0) 1.5511 (1.16) 1.7410 (1.0) 0.0801 (1.0) 144;684 504.3878 (1.0) 7201 1
test_reify_chain_stream[300] 1.7059 (1.12) 18.6020 (1.0) 2.1237 (1.07) 1.3389 (1.0) 1.9260 (1.11) 0.1020 (1.27) 118;585 470.8745 (0.93) 6416 1
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------- benchmark 'reify_chain size=35': 2 tests --------------------------------------------------------------------------------
Name (time in us) Min Max Mean StdDev Median IQR Outliers OPS (Kops/s) Rounds Iterations
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
test_reify_chain_stream[35] 129.2780 (1.0) 868.1510 (1.02) 190.0433 (1.11) 36.2784 (1.41) 179.5690 (1.08) 21.5360 (2.30) 1535;1455 5.2620 (0.90) 26072 1
test_reify_chain_stack[35] 150.7850 (1.17) 853.7920 (1.0) 170.5166 (1.0) 25.7944 (1.0) 165.8500 (1.0) 9.3530 (1.0) 3724;5480 5.8645 (1.0) 81286 1
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
------------------------------------------- benchmark 'reify_chain size=5000': 1 tests ------------------------------------------
Name (time in ms) Min Max Mean StdDev Median IQR Outliers OPS Rounds Iterations
---------------------------------------------------------------------------------------------------------------------------------
test_reify_chain_stream_large[5000] 46.9073 86.9737 52.9724 6.6919 49.6787 3.9609 68;68 18.8778 292 1
---------------------------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------- benchmark 'unify_chain size=10': 2 tests -------------------------------------------------------------------------------
Name (time in us) Min Max Mean StdDev Median IQR Outliers OPS (Kops/s) Rounds Iterations
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
test_unify_chain_stream[10] 77.6280 (1.0) 307.9130 (1.0) 86.7625 (1.0) 17.5355 (1.20) 82.7525 (1.0) 1.7290 (1.0) 809;1736 11.5257 (1.0) 15524 1
test_unify_chain_stack[10] 92.9890 (1.20) 309.8770 (1.01) 104.2017 (1.20) 14.6694 (1.0) 101.0160 (1.22) 4.2368 (2.45) 3657;6651 9.5968 (0.83) 73379 1
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
------------------------------------------- benchmark 'unify_chain size=1000': 1 tests ------------------------------------------
Name (time in ms) Min Max Mean StdDev Median IQR Outliers OPS Rounds Iterations
---------------------------------------------------------------------------------------------------------------------------------
test_unify_chain_stream_large[1000] 27.3518 65.5924 31.1374 4.2563 29.5148 3.5286 38;35 32.1158 496 1
---------------------------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------- benchmark 'unify_chain size=300': 2 tests --------------------------------------------------------------------------
Name (time in ms) Min Max Mean StdDev Median IQR Outliers OPS Rounds Iterations
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
test_unify_chain_stream[300] 3.6957 (1.0) 13.1876 (1.0) 4.4439 (1.0) 1.0719 (1.42) 4.2080 (1.0) 0.2410 (1.67) 51;95 225.0298 (1.0) 1114 1
test_unify_chain_stack[300] 4.2952 (1.16) 13.4294 (1.02) 4.7732 (1.07) 0.7555 (1.0) 4.6623 (1.11) 0.1446 (1.0) 36;136 209.5024 (0.93) 2911 1
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------- benchmark 'unify_chain size=35': 2 tests ---------------------------------------------------------------------------------
Name (time in us) Min Max Mean StdDev Median IQR Outliers OPS (Kops/s) Rounds Iterations
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
test_unify_chain_stream[35] 285.6880 (1.0) 934.9690 (1.0) 324.5402 (1.0) 40.8338 (1.0) 319.8520 (1.0) 20.4375 (1.0) 962;1159 3.0813 (1.0) 24331 1
test_unify_chain_stack[35] 345.2770 (1.21) 1,088.3650 (1.16) 407.9067 (1.26) 52.2263 (1.28) 396.6640 (1.24) 20.6560 (1.01) 2054;3027 2.4515 (0.80) 37594 1
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
--------------------------------------------- benchmark 'unify_chain size=5000': 1 tests ---------------------------------------------
Name (time in ms) Min Max Mean StdDev Median IQR Outliers OPS Rounds Iterations
--------------------------------------------------------------------------------------------------------------------------------------
test_unify_chain_stream_large[5000] 555.2733 754.9897 605.4949 50.6124 591.1251 61.4030 2;2 1.6515 26 1
--------------------------------------------------------------------------------------------------------------------------------------
Legend:
Outliers: 1 Standard Deviation from Mean; 1.5 IQR (InterQuartile Range) from 1st Quartile and 3rd Quartile.
OPS: Operations Per Second, computed as 1 / Mean
```
</p>
</details>
## About
This project is a fork of [`unification`](https://github.com/mrocklin/unification/).
## Development
Install the development dependencies:
```bash
$ pip install -r requirements.txt
```
Set up `pre-commit` hooks:
```bash
$ pre-commit install --install-hooks
```
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"description": "# Logical Unification\n\n[](https://travis-ci.org/pythological/unification) [](https://coveralls.io/github/pythological/unification?branch=main) [](https://pypi.org/project/logical-unification/)\n\n[Logical unification](https://en.wikipedia.org/wiki/Unification_(computer_science)) in Python, extensible via dispatch.\n\n## Installation\n\nUsing `pip`:\n```bash\npip install logical-unification\n```\n\nTo install from source:\n```bash\ngit clone git@github.com:pythological/unification.git\ncd unification\npip install -r requirements.txt\n```\n\nTests can be run with the provided `Makefile`:\n```bash\nmake check\n```\n\n## Examples\n\n`unification` has built-in support for unifying most Python data types via the function `unify`:\n\n```python\n>>> from unification import *\n>>> unify(1, 1)\n{}\n>>> unify(1, 2)\nFalse\n>>> x = var()\n>>> unify((1, x), (1, 2))\n{~x: 2}\n>>> unify((x, x), (1, 2))\nFalse\n```\n\nUnifiable objects containing logic variables can also be reified using `reify`:\n\n```python\n>>> reify((1, x), {x: 2})\n(1, 2)\n```\n\nAnd most Python data structures:\n\n``` python\n>>> unify({\"a\": 1, \"b\": 2}, {\"a\": x, \"b\": 2})\n{~x: 1}\n>>> unify({\"a\": 1, \"b\": 2}, {\"a\": x, \"b\": 2, \"c\": 3})\nFalse\n>>> from collections import namedtuples\n>>> ntuple = namedtuple(\"ntuple\", (\"a\", \"b\"))\n>>> unify(ntuple(1, 2), ntuple(x, 2))\n{~x: 1}\n```\n\nCustom classes can be made \"unifiable\" with the `unifiable` decorator:\n\n```python\n@unifiable\nclass Account(object):\n def __init__(self, id, name, balance):\n self.id = id\n self.name = name\n self.balance = balance\n\n>>> data = [Account(1, 'Alice', 100),\n Account(2, 'Bob', 0),\n Account(2, 'Charlie', 0),\n Account(2, 'Denis', 400),\n Account(2, 'Edith', 500)]\n>>> id, name, balance = var('id'), var('name'), var('balance')\n>>> [unify(Account(id, name, balance), acct) for acct in data]\n[{~name: 'Alice', ~balance: 100, ~id: 1},\n{~name: 'Bob', ~balance: 0, ~id: 2},\n{~name: 'Charlie', ~balance: 0, ~id: 2},\n{~name: 'Denis', ~balance: 400, ~id: 2},\n{~name: 'Edith', ~balance: 500, ~id: 2}]\n>>> [unify(Account(id, name, 0), acct) for acct in data]\n[False,\n{~name: 'Bob', ~id: 2},\n{~name: 'Charlie', ~id: 2},\nFalse,\nFalse]\n```\n\n`unification` also supports function dispatch through pattern matching:\n\n```python\n>> from unification.match import *\n>>> n = var('n')\n\n@match(0)\ndef fib(n):\n return 0\n\n\n@match(1)\ndef fib(n):\n return 1\n\n\n@match(n)\ndef fib(n):\n return fib(n - 1) + fib(n - 2)\n\n>>> map(fib, [0, 1, 2, 3, 4, 5, 6, 7, 8, 0])\n[0, 1, 1, 2, 3, 5, 8, 13, 21, 34]\n```\n\nThe pattern matching can be fairly complex:\n\n```python\n>> name, amount = var('name'), var('amount')\n\n@match({'status': 200, 'data': {'name': name, 'credit': amount}})\ndef respond(name, amount):\n balance[name] += amount\n\n\n@match({'status': 200, 'data': {'name': name, 'debit': amount}})\ndef respond(name, amount):\n balance[name] -= amount\n\n\n@match({'status': 404})\ndef respond():\n print(\"Bad Request\")\n\n```\n\nSee the full example in the [examples directory](https://github.com/pythological/unification#examples).\n\n\n## Performance and Reliability\n\n`unification`'s current design allows for unification and reification of nested structures that would otherwise break the Python stack recursion limit. It uses a generator-based design to \"stream\" the unifications and reifications.\n\nBelow are some stack vs. stream benchmarks that demonstrate how well the stream-based approach scales against the stack-based approach in terms of unifying and reifying deeply nested lists containing integers. These benchmarks were generated from the tests in `tests/test_benchmarks.py` using CPython 3.7.3.\n\n<details><summary>Stack vs. stream benchmarks</summary>\n<p>\n\n```python\n-------------------------------------------------------------------------------- benchmark 'reify_chain size=10': 2 tests -------------------------------------------------------------------------------\nName (time in us) Min Max Mean StdDev Median IQR Outliers OPS (Kops/s) Rounds Iterations\n---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\ntest_reify_chain_stack[10] 41.0790 (1.0) 545.1940 (3.20) 52.9087 (1.07) 9.7964 (1.04) 50.8650 (1.08) 6.4301 (8.37) 11815;10849 18.9005 (0.93) 260164 1\ntest_reify_chain_stream[10] 42.4410 (1.03) 170.5540 (1.0) 49.3080 (1.0) 9.3993 (1.0) 47.2400 (1.0) 0.7680 (1.0) 14962;102731 20.2807 (1.0) 278113 1\n---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n\n------------------------------------------ benchmark 'reify_chain size=1000': 1 tests -----------------------------------------\nName (time in ms) Min Max Mean StdDev Median IQR Outliers OPS Rounds Iterations\n-------------------------------------------------------------------------------------------------------------------------------\ntest_reify_chain_stream_large[1000] 7.7722 28.2579 10.0723 2.5087 9.4899 0.3106 70;155 99.2820 1528 1\n-------------------------------------------------------------------------------------------------------------------------------\n\n------------------------------------------------------------------------- benchmark 'reify_chain size=300': 2 tests --------------------------------------------------------------------------\nName (time in ms) Min Max Mean StdDev Median IQR Outliers OPS Rounds Iterations\n----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\ntest_reify_chain_stack[300] 1.5183 (1.0) 22.1821 (1.19) 1.9826 (1.0) 1.5511 (1.16) 1.7410 (1.0) 0.0801 (1.0) 144;684 504.3878 (1.0) 7201 1\ntest_reify_chain_stream[300] 1.7059 (1.12) 18.6020 (1.0) 2.1237 (1.07) 1.3389 (1.0) 1.9260 (1.11) 0.1020 (1.27) 118;585 470.8745 (0.93) 6416 1\n----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n\n--------------------------------------------------------------------------------- benchmark 'reify_chain size=35': 2 tests --------------------------------------------------------------------------------\nName (time in us) Min Max Mean StdDev Median IQR Outliers OPS (Kops/s) Rounds Iterations\n-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\ntest_reify_chain_stream[35] 129.2780 (1.0) 868.1510 (1.02) 190.0433 (1.11) 36.2784 (1.41) 179.5690 (1.08) 21.5360 (2.30) 1535;1455 5.2620 (0.90) 26072 1\ntest_reify_chain_stack[35] 150.7850 (1.17) 853.7920 (1.0) 170.5166 (1.0) 25.7944 (1.0) 165.8500 (1.0) 9.3530 (1.0) 3724;5480 5.8645 (1.0) 81286 1\n-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n\n------------------------------------------- benchmark 'reify_chain size=5000': 1 tests ------------------------------------------\nName (time in ms) Min Max Mean StdDev Median IQR Outliers OPS Rounds Iterations\n---------------------------------------------------------------------------------------------------------------------------------\ntest_reify_chain_stream_large[5000] 46.9073 86.9737 52.9724 6.6919 49.6787 3.9609 68;68 18.8778 292 1\n---------------------------------------------------------------------------------------------------------------------------------\n\n------------------------------------------------------------------------------- benchmark 'unify_chain size=10': 2 tests -------------------------------------------------------------------------------\nName (time in us) Min Max Mean StdDev Median IQR Outliers OPS (Kops/s) Rounds Iterations\n--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\ntest_unify_chain_stream[10] 77.6280 (1.0) 307.9130 (1.0) 86.7625 (1.0) 17.5355 (1.20) 82.7525 (1.0) 1.7290 (1.0) 809;1736 11.5257 (1.0) 15524 1\ntest_unify_chain_stack[10] 92.9890 (1.20) 309.8770 (1.01) 104.2017 (1.20) 14.6694 (1.0) 101.0160 (1.22) 4.2368 (2.45) 3657;6651 9.5968 (0.83) 73379 1\n--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n\n------------------------------------------- benchmark 'unify_chain size=1000': 1 tests ------------------------------------------\nName (time in ms) Min Max Mean StdDev Median IQR Outliers OPS Rounds Iterations\n---------------------------------------------------------------------------------------------------------------------------------\ntest_unify_chain_stream_large[1000] 27.3518 65.5924 31.1374 4.2563 29.5148 3.5286 38;35 32.1158 496 1\n---------------------------------------------------------------------------------------------------------------------------------\n\n------------------------------------------------------------------------- benchmark 'unify_chain size=300': 2 tests --------------------------------------------------------------------------\nName (time in ms) Min Max Mean StdDev Median IQR Outliers OPS Rounds Iterations\n----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\ntest_unify_chain_stream[300] 3.6957 (1.0) 13.1876 (1.0) 4.4439 (1.0) 1.0719 (1.42) 4.2080 (1.0) 0.2410 (1.67) 51;95 225.0298 (1.0) 1114 1\ntest_unify_chain_stack[300] 4.2952 (1.16) 13.4294 (1.02) 4.7732 (1.07) 0.7555 (1.0) 4.6623 (1.11) 0.1446 (1.0) 36;136 209.5024 (0.93) 2911 1\n----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n\n--------------------------------------------------------------------------------- benchmark 'unify_chain size=35': 2 tests ---------------------------------------------------------------------------------\nName (time in us) Min Max Mean StdDev Median IQR Outliers OPS (Kops/s) Rounds Iterations\n------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\ntest_unify_chain_stream[35] 285.6880 (1.0) 934.9690 (1.0) 324.5402 (1.0) 40.8338 (1.0) 319.8520 (1.0) 20.4375 (1.0) 962;1159 3.0813 (1.0) 24331 1\ntest_unify_chain_stack[35] 345.2770 (1.21) 1,088.3650 (1.16) 407.9067 (1.26) 52.2263 (1.28) 396.6640 (1.24) 20.6560 (1.01) 2054;3027 2.4515 (0.80) 37594 1\n------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------\n\n--------------------------------------------- benchmark 'unify_chain size=5000': 1 tests ---------------------------------------------\nName (time in ms) Min Max Mean StdDev Median IQR Outliers OPS Rounds Iterations\n--------------------------------------------------------------------------------------------------------------------------------------\ntest_unify_chain_stream_large[5000] 555.2733 754.9897 605.4949 50.6124 591.1251 61.4030 2;2 1.6515 26 1\n--------------------------------------------------------------------------------------------------------------------------------------\n\nLegend:\n Outliers: 1 Standard Deviation from Mean; 1.5 IQR (InterQuartile Range) from 1st Quartile and 3rd Quartile.\n OPS: Operations Per Second, computed as 1 / Mean\n```\n\n</p>\n</details>\n\n## About\n\nThis project is a fork of [`unification`](https://github.com/mrocklin/unification/).\n\n## Development\n\nInstall the development dependencies:\n\n```bash\n$ pip install -r requirements.txt\n```\n\nSet up `pre-commit` hooks:\n\n```bash\n$ pre-commit install --install-hooks\n```",
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